Individual stocks don’t have beneficiaries~!~ Just rename the brokerage account in the name of your Revocable Living Trust, and have the brokerage firm hold the stocks in that account. (If you have old stock certificates, this is the easiest way to change the name on them to the name of the trust. Or you can send them into the Transfer Agent — bank — listed on the back of the certificate, along with the relevant trust enabling papers.)
If you are mailing paper stock certificates, use registered mail, w return receipt requested.
There is no tax consequence to asking your broker to re-name your account in the name of your RLT– but you will need to provide the pages of the trust document that give you authorization. Ask the attorney who created the trust for these pages, or several copies if you have multiple accounts.